arxiv: 2604.24866 · v1 · submitted 2026-04-27 · 🌌 astro-ph.IM · gr-qc· physics.geo-ph

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Seismic background mitigation with the Lunar Gravitational-wave Antenna

Han Yan , Jan Harms

Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:21 UTC · model grok-4.3

classification 🌌 astro-ph.IM gr-qcphysics.geo-ph

keywords seismic noise mitigationlunar gravitational wave antennaLGWAseismic correlationBessel functionsignal-to-noise ratioarray processing

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The pith

Optimal spacing of two seismic stations on the Moon can reduce equivalent seismic noise by a factor of 2.3 at 0.3 Hz for gravitational-wave measurements.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives analytical expressions for the best possible signal-to-noise ratio when combining data from two seismic stations in an isotropic random Gaussian field. It shows that the amount of noise reduction depends on how far apart the stations are placed relative to the length scale over which seismic motions stay correlated. With the right spacing the equivalent seismic noise amplitude spectrum density improves by roughly a factor of 2.3 at 0.3 Hz compared with a single station, and the spectrum displays clear oscillations set by the underlying correlation shape. This matters because lunar gravitational-wave antennas such as LGWA measure the Moon's response to gravitational waves and are limited by seismic background; showing a concrete way to suppress that background by array processing makes the detector concept more realistic.

Core claim

We derive the analytical expressions for the optimal squared signal-to-noise ratio considering two seismic stations in an isotropic, random, Gaussian seismic field. Our numerical analysis reveals that the capacity to mitigate the seismic noise critically depends on the distance between the two stations relative to the seismic-correlation length. We demonstrate that optimal placement of the two stations can yield significant improvements in the equivalent seismic noise amplitude spectrum density (ASD), approximately a factor of 2.3 at 0.3 Hz, compared to the measurement with a single station. The equivalent ASD of the seismic noise also exhibits distinct oscillatory and mitigation features.

What carries the argument

The Bessel-function form of the spatial correlation in an isotropic random Gaussian seismic field, which determines how signals from two stations are optimally combined to maximize the signal-to-noise ratio.

If this is right

Optimal station separation relative to the seismic correlation length produces the largest noise reduction.
The equivalent seismic noise ASD improves by a factor of approximately 2.3 at 0.3 Hz under optimal placement.
The noise spectrum after combination displays oscillatory features set by the Bessel correlation structure.
Array processing with two stations distinguishes gravitational-wave signals from the seismic background more effectively than a single station.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Extending the same correlation model to three or more stations could yield further noise suppression beyond the two-station case.
Direct measurements of actual lunar seismic correlations would allow the analytical expressions to be recalibrated for site-specific conditions.
The same optimal-combination approach may apply to other array-based gravitational-wave concepts on the Moon or on Earth where correlated noise dominates.

Load-bearing premise

The lunar seismic background is an isotropic random Gaussian field whose correlations are completely described by a Bessel-function form.

What would settle it

Seismic data recorded on the Moon showing correlation lengths or directional dependence that deviate strongly from the assumed Bessel form at frequencies near 0.3 Hz would eliminate the predicted factor-of-2.3 improvement.

Figures

Figures reproduced from arXiv: 2604.24866 by Han Yan, Jan Harms.

**Figure 1.** Figure 1: FIG. 1. Array configuration scenario view at source ↗

**Figure 3.** Figure 3: FIG. 3. Sky-averaged SNR view at source ↗

read the original abstract

Lunar gravitational-wave (GW) detectors relying on the measurement of the response of the Moon to GWs are susceptible to a seismic background, which might pose a fundamental sensitivity limitation. The Lunar Gravitational-wave Antenna (LGWA) was conceived as an array of accelerometers with the idea that data can be processed to distinguish between a GW signal and the seismic background. As a result, the seismic noise of the GW measurement would be mitigated. However, so far, no quantitative assessment of the mitigation of the seismic background has been provided. In this article, we derive the analytical expressions for the optimal squared signal-to-noise ratio considering two seismic stations in an isotropic, random, Gaussian seismic field. Our numerical analysis reveals that the capacity to mitigate the seismic noise critically depends on the distance between the two stations relative to the seismic-correlation length. We demonstrate that optimal placement of the two stations can yield significant improvements in the equivalent seismic noise amplitude spectrum density (ASD), approximately a factor of 2.3 at 0.3 Hz, compared to the measurement with a single station. The equivalent ASD of the seismic noise also exhibits distinct oscillatory and mitigation features arising from the Bessel-function structure of the noise correlation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper supplies the first analytical expressions for optimal two-station seismic noise reduction in lunar GW detectors and shows a model-dependent factor of 2.3 ASD improvement at 0.3 Hz.

read the letter

The main point is that the authors derive closed-form expressions for the optimal squared SNR when combining two seismic stations in an isotropic random Gaussian field whose correlation follows a Bessel function of the station separation. They then plot the resulting equivalent noise ASD versus distance and frequency, finding that optimal placement can cut the noise by about 2.3 at 0.3 Hz relative to a single station, with clear oscillatory features tied to the correlation length. That is new; the abstract correctly notes that no prior quantitative treatment existed for this specific mitigation approach in the LGWA context. The derivation itself is direct: it inverts the 2x2 noise covariance matrix whose off-diagonals are the Bessel term and assumes the GW signal vector is known and deterministic. The numerical results follow cleanly from those steps and give a concrete scaling with distance that array designers can use. The central limitation is that the entire gain, including the factor 2.3 and the oscillations, is locked to the exact isotropic Gaussian plus J0 correlation model. Lunar seismic fields include scattering, layering, and discrete moonquake events that likely violate those assumptions, yet the paper offers no checks against anisotropy, non-Gaussianity, or alternative correlation forms. It also stops at two stations. This is useful reading for the small group working on lunar GW concepts or seismic array processing for low-frequency detectors. Anyone planning station layouts will want the distance-dependent expressions even if they later test them against more realistic simulations. I would send it to referees; the calculation is self-contained and the result is new, so it merits external review even though the model assumptions will need more scrutiny in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript derives analytical expressions for the optimal squared signal-to-noise ratio using two seismic stations in an isotropic, random, Gaussian seismic field whose spatial correlation is given by a Bessel function. Numerical results show that seismic-noise mitigation for the Lunar Gravitational-wave Antenna depends on station separation relative to the correlation length, with optimal placement yielding an approximately factor-of-2.3 reduction in equivalent seismic noise ASD at 0.3 Hz together with distance-dependent oscillatory features.

Significance. If the stated statistical model of the seismic field is applicable, the work supplies a clean, closed-form framework for quantifying array-based seismic mitigation in lunar GW detectors and identifies concrete guidance for station placement. The analytical SNR derivation and the explicit link between mitigation performance and the Bessel correlation structure constitute clear strengths.

major comments (2)

[Numerical analysis and optimal-combination derivation] The factor-of-2.3 ASD improvement at 0.3 Hz and the reported oscillatory mitigation features are obtained by inverting the 2×2 noise covariance matrix whose off-diagonal elements are J0(d/λ). This result is load-bearing for the central claim; the manuscript should therefore include at least a brief sensitivity analysis or explicit statement of the range of validity when the actual lunar seismic field deviates from perfect isotropy, Gaussianity, or the exact Bessel functional form (e.g., due to scattering or layering).
[Optimal SNR derivation] The optimal linear combination is derived under the assumption that the GW-induced signal vector is known and deterministic. Because real GW signals have unknown direction and polarization, the practical SNR gain may be lower; the paper should quantify or bound the degradation under a stochastic or unknown-signal model.

minor comments (2)

[Abstract] The abstract states “approximately a factor of 2.3 at 0.3 Hz” without specifying the exact station separation or correlation length used; adding these parameters would improve reproducibility.
[Figures] Figure captions should explicitly state the correlation length λ and the frequency at which each curve is evaluated so that the distance-dependent oscillations can be interpreted without reference to the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the recommendation of minor revision. We address each major comment below and have updated the manuscript accordingly.

read point-by-point responses

Referee: [Numerical analysis and optimal-combination derivation] The factor-of-2.3 ASD improvement at 0.3 Hz and the reported oscillatory mitigation features are obtained by inverting the 2×2 noise covariance matrix whose off-diagonal elements are J0(d/λ). This result is load-bearing for the central claim; the manuscript should therefore include at least a brief sensitivity analysis or explicit statement of the range of validity when the actual lunar seismic field deviates from perfect isotropy, Gaussianity, or the exact Bessel functional form (e.g., due to scattering or layering).

Authors: We agree that the assumptions of the seismic-field model are central to the quantitative claims. The revised manuscript now contains an explicit statement in the Discussion section that the derived improvement factor and oscillatory features are obtained under the assumptions of statistical isotropy, Gaussianity, and the exact Bessel correlation function. We further note that deviations arising from scattering or layering would alter the off-diagonal covariance terms and therefore the achievable mitigation. A full numerical sensitivity study is not possible with currently available lunar seismic data; the closed-form expressions we provide, however, constitute a transparent baseline that future work can extend once more detailed correlation measurements exist. revision: yes
Referee: [Optimal SNR derivation] The optimal linear combination is derived under the assumption that the GW-induced signal vector is known and deterministic. Because real GW signals have unknown direction and polarization, the practical SNR gain may be lower; the paper should quantify or bound the degradation under a stochastic or unknown-signal model.

Authors: The derivation yields the maximum attainable SNR for a perfectly known deterministic signal vector (i.e., fixed direction and polarization). This quantity therefore represents the theoretical upper bound on noise mitigation with the two-station configuration. For signals whose parameters are unknown a priori, the effective gain depends on the detection statistic (e.g., marginalization over sky location and polarization). We have added a concise paragraph in the Conclusions acknowledging this distinction and stating that the reported factor of ~2.3 is the ideal-case improvement. A quantitative bound on the degradation would require a specific GW population model and search pipeline, which lies outside the scope of the present work whose focus is the characterization of the seismic-noise covariance. revision: partial

Circularity Check

0 steps flagged

Derivation is self-contained from model assumptions to quantitative predictions

full rationale

The paper begins with the explicit modeling assumption of an isotropic, random, Gaussian seismic field whose spatial correlation is given by the Bessel function J0(d/λ). It then derives the optimal linear combination of two stations by inverting the 2x2 noise covariance matrix (whose off-diagonals are exactly that J0 term) to maximize the squared SNR for a deterministic GW signal. The reported factor-of-2.3 ASD improvement at 0.3 Hz and the oscillatory features are obtained by direct numerical evaluation of the resulting closed-form SNR expression as a function of station separation. No parameter is fitted to data, no result is defined in terms of itself, and no load-bearing step reduces to a self-citation or prior ansatz by the same authors. The entire chain is a standard forward derivation whose outputs are conditional on the stated statistical model but not equivalent to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the seismic field is isotropic, random, and Gaussian; no free parameters are introduced or fitted, and no new physical entities are postulated.

axioms (1)

domain assumption The seismic background is an isotropic, random, Gaussian field
This statistical model is invoked to obtain the two-station correlation function and the optimal SNR expressions.

pith-pipeline@v0.9.0 · 5509 in / 1337 out tokens · 153030 ms · 2026-05-07T17:21:59.712774+00:00 · methodology

discussion (0)

Reference graph

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